binom.bayes: Binomial confidence intervals using Bayesian inference

Description

Uses a beta prior on the probability of success for a binomial
distribution, determines a two-sided confidence interval from a beta
posterior. A plotting function is also provided to show the
probability regions defined by each confidence interval.

The type of confidence interval (see Details).

prior.shape1

The value of the first shape parameter to be used in the prior beta.

prior.shape2

The value of the second shape parameter to be used in the prior beta.

tol

A tolerance to be used in determining the highest probability density interval.

maxit

Maximum number of iterations to be used in determining
the highest probability interval.

bayes

The output data.frame from binom.bayes.

npoints

The number of points to use to draw the density
curves. Higher numbers give smoother densities.

fill.central

The color for the central density.

fill.lower,fill.upper

The color(s) for the upper and lower
density.

alpha

The alpha value for controlling transparency.

...

Ignored.

Details

Using the conjugate beta prior on the distribution of p (the
probability of success) in a binomial experiment, constructs a
confidence interval from the beta posterior. From Bayes theorem the
posterior distribution of p given the data x is:

p|x ~ Beta(x + prior.shape1, n - x + prior.shape2)

The default prior is Jeffrey's prior which is a Beta(0.5, 0.5)
distribution. Thus the posterior mean is (x + 0.5)/(n + 1).

The default type of interval constructed is "highest" which computes
the highest probability density (hpd) interval which assures the
shortest interval possible. The hpd intervals will achieve a
probability that is within tol of the specified conf.level. Setting
type to "central" constructs intervals that have equal tail
probabilities.

If 0 or n successes are observed, a one-sided confidence interval is
returned.

Value

For binom.bayes, a data.frame containing the observed
proportions and the lower and upper bounds of the confidence interval.

For binom.bayes.densityplot, a ggplot object that can
printed to a graphics device, or have additional layers added.